2.128   ODE No. 128

1. Problem in Latex
2. Mathematica input
3. Maple input

$$-f(x)g(x^{a}y(x))+ay(x)+x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 4.2919 (sec), leaf count = 39

$$\text{Solve}[{\int }_1^{x^{a}y(x)}\frac{1}{g(K[1])}dK[1]={\int }_1^{x}K[2{]}^{a-1}f(K[2])dK[2]+c_1,y(x)]$$

✓ Maple : cpu = 0.273 (sec), leaf count = 33

$$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\int f\left(x\right)x^{a-1}\mathrm{d}x+{\int }^{\mathit{\_}\mathit{Z}}{\left(g\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}{x^a}\}$$